I have children the same age as you and am very pleased with the education my children get. The key is being able to afford to live in a top ranked school district. The school my kids go to has very involved parents which make up for shortfalls and are the biggest reason the schools are top ranked. Parents that value education, are motivated to support it AND are able to support it are crucial. There are always parent voluneteers in the class room and there are constant fundraisers. We continuously donate school supplies, provide rides for field trips and support our schools in any way possible. I am very satisfied with the quality of their education.
As a footnote I grew up in another part of the country and attended public schools that are consistently among the best in the country so I believe that I have a good basis for comparison.
Another footnote, while I was fortunate to attend very privileged public schools, the schools we competed with in sports were extremely underprivileged and in some of the most dangerous cities in America.
Sadly, if you are not as fortunate (and make no mistake I feel VERY fortunate) to live in such an area I suspect much of what you fear is true. However, it is likely true for most areas of the the country.